Computing Ordinary Demands Solve for 2 simultaneous equations Tangency Budget constraint The conditions may be obtained by using the Lagrangian multiplier method ie constrained optimization In calculus
Computing Ordinary Demands Solve for 2 simultaneous equations. –Tangency –Budget constraint The conditions may be obtained by using the Lagrangian multiplier method, i.e., constrained optimization in calculus
Computing Ordinary Demands How can this information be used to locate( X,*, x *)for given p1, p2 and m?
Computing Ordinary Demands How can this information be used to locate (x1 *,x2 *) for given p1 , p2 and m?
Computing Ordinary demands a Cobb-Douglas Example Suppose that the consumer has Cobb-Douglas preferences. U(x1,X2)=X1x2
Computing Ordinary Demands - a Cobb-Douglas Example. Suppose that the consumer has Cobb-Douglas preferences. U x x x x a b ( , ) 1 2 = 1 2
Computing Ordinary demands a Cobb-Douglas Example Suppose that the consumer has Cobb-Douglas preferences. U(x1, x2)=xix Then MU- OU ax1 X ox1 Ox2bx月x21 MU,=列U
Computing Ordinary Demands - a Cobb-Douglas Example. Suppose that the consumer has Cobb-Douglas preferences. Then U x x x x a b ( , ) 1 2 = 1 2 MU U x ax x a b 1 1 1 1 = = 2 − MU U x bx x a b 2 2 1 2 1 = = −
Computing Ordinary demands a Cobb-Douglas Example So the mrs is MRS=ua2 QUox ax x6 ax2 dx1 Oula bxayb-1 bx1
Computing Ordinary Demands - a Cobb-Douglas Example. So the MRS is MRS dx dx U x U x ax x bx x ax bx a b a b = = − = − = − − − 2 1 1 2 1 1 2 1 2 1 2 1 / /